Our final warning [in Chapter 18] has to do with your
general opinion of ANCOVA-based studies as compared with ANOVA-based studies.
Because ANCOVA is more complex (due to the involvement of a larger number
of variables and assumptions), many consumers of the research literature
hold the opinion that data-based claims are more trustworthy when they
are based upon ANCOVA rather than ANOVA. We strongly encourage you to
refrain from adopting this unjustified point of view.

Although ANCOVA (as compared with ANOVA) does, in fact,
involve more complexities in terms of what is involved both on and beneath
the surface, it is an extremely delicate instrument. To provide meaningful
results, ANCOVA must be used very carefully--with attention paid to important
assumptions, with focus directed at the appropriate set of sample means,
and with concern over the correct way to draw inferences from ANCOVA's
F-tests. Because of its complexity, ANCOVA affords its users more opportunities
to make mistakes than does ANOVA.

If used skillfully, ANCOVA can be of great assistance
to applied researchers. If not used skillfully, however, ANCOVA can be
dangerous. We say that because of the unfortunate tendency of many people
to think of complexity as being an inherent virtue. In statistics, that
is often not the case. As pointed out earlier in the chapter, the interpretation
of ANCOVA F-tests is problematic whenever the groups being compared have
been formed in a nonrandom fashion--and this statement holds true even
if (1) multiple covariate variables are involved, and (2) full attention
is directed to all underlying assumptions. In contrast, it would be much
easier to interpret the results generated by the application of ANOVA
to the data provided by subjects who have been randomly assigned to comparison
groups. Care is required, of course, whenever you attempt to interpret
the outcome of any inferential test. Our point is simply that ANCOVA,
because of its complexity as compared to ANOVA, demands a higher--not
lower--level of care on your part when you encounter its results.